Details

sample175.0ms

Algorithm

intervals

Results

69.0ms	834×	body	80	nan
27.0ms	329×	body	80	valid
18.0ms	32×	body	1280	nan
12.0ms	94×	body	80	overflowed
12.0ms	28×	body	640	nan
5.0ms	17×	body	320	nan
1.0ms	3×	body	160	nan

simplify40.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	29	8
1	59	8
2	119	8
3	325	8
4	1044	8
5	5001	8

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 0.4b

Counts

2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
0.2b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
0.2b	(* (* 2.0 PI) n)
0.3b	(/ 1.0 (sqrt k))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-sqr-sqrt`
55×	`times-frac`
49×	`*-un-lft-identity`
46×	`add-exp-log`
43×	`add-cube-cbrt`
23×	`associate-l` `sqrt-prod`
22×	`prod-exp`
19×	`pow-unpow`
16×	`add-cbrt-cube`
15×	`pow1`
9×	`pow-exp`
8×	`associate-r`
6×	`div-exp` `pow-prod-down` `associate-/r*` `unswap-sqr`
5×	`cbrt-unprod` `sqr-pow`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `pow-pow` `div-sub` `div-inv` `associate-/l*` `distribute-lft-out--` `pow-sub` `difference-of-squares`
2×	`cbrt-undiv` `unpow-prod-down` `*-commutative`
1×	`frac-times` `frac-2neg` `associate-r/` `associate-l/` `clear-num`

Counts

4 → 157

Calls

4 calls:

11.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
9.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
5.0ms	(* (* 2.0 PI) n)
4.0ms	(/ 1.0 (sqrt k))

series542.0ms

Counts

4 → 12

Calls

4 calls:

320.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
145.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
32.0ms	(* (* 2.0 PI) n)
44.0ms	(/ 1.0 (sqrt k))

simplify102.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 2 (86.0ms)

Iter	Nodes	Cost
0	981	1502
1	4022	1398
2	5002	1383

prune432.0ms

Filtered

169 candidates to 119 candidates (70.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	160	9	169
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	161	9	170

Merged error: 0.0b

Counts

170 → 9

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))
0.2b	(* (* 2.0 PI) n)
0.2b	(* (* 2.0 PI) n)
0.2b	(/ (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

176×	`add-exp-log`
105×	`prod-exp`
39×	`pow-exp`
36×	`div-exp`
26×	`add-cbrt-cube`
20×	`pow1`
13×	`add-sqr-sqrt` `pow-to-exp` `add-cube-cbrt` `pow-unpow` `*-un-lft-identity`
10×	`times-frac` `cbrt-unprod`
9×	`pow-prod-down`
6×	`associate-r`
4×	`cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-pow`
2×	`associate-l` `*-commutative` `div-inv`
1×	`unpow-prod-down` `frac-2neg` `clear-num` `associate-/r` `associate-/l` `sqr-pow`

Counts

4 → 126

Calls

4 calls:

6.0ms	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))
5.0ms	(* (* 2.0 PI) n)
5.0ms	(* (* 2.0 PI) n)
10.0ms	(/ (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))))

series1.3s

Counts

4 → 12

Calls

4 calls:

253.0ms	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))
31.0ms	(* (* 2.0 PI) n)
35.0ms	(* (* 2.0 PI) n)
1.0s	(/ (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))))

simplify101.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 2 (86.0ms)

Iter	Nodes	Cost
0	935	1406
1	4012	1247
2	5001	1237

prune259.0ms

Filtered

138 candidates to 68 candidates (49.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	138	0	138
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	138	9	147

Merged error: 0.0b

Counts

147 → 9

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (* (* (* 2.0 PI) (sqrt n)) (sqrt n)) (/ (- 1.0 k) 2.0))
0.3b	(/ 1.0 (sqrt k))
0.3b	(* (* 2.0 PI) (sqrt n))
0.4b	(* (* (* 2.0 PI) (sqrt n)) (sqrt n))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt` `*-un-lft-identity`
33×	`times-frac`
32×	`add-cube-cbrt`
30×	`add-exp-log`
28×	`pow1`
20×	`add-cbrt-cube`
19×	`pow-unpow`
18×	`sqrt-prod`
15×	`pow-prod-down` `prod-exp`
12×	`associate-r`
9×	`cbrt-unprod`
6×	`associate-/r*`
4×	`expm1-log1p-u` `pow-pow` `pow-exp` `log1p-expm1-u` `add-log-exp`
3×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
2×	`associate-l` `*-commutative` `div-inv`
1×	`cbrt-undiv` `pow-to-exp` `unpow-prod-down` `frac-2neg` `div-sub` `div-exp` `clear-num` `pow-sub` `sqr-pow`

Counts

4 → 130

Calls

4 calls:

12.0ms	(pow (* (* (* 2.0 PI) (sqrt n)) (sqrt n)) (/ (- 1.0 k) 2.0))
4.0ms	(/ 1.0 (sqrt k))
6.0ms	(* (* 2.0 PI) (sqrt n))
9.0ms	(* (* (* 2.0 PI) (sqrt n)) (sqrt n))

series360.0ms

Counts

4 → 12

Calls

4 calls:

195.0ms	(pow (* (* (* 2.0 PI) (sqrt n)) (sqrt n)) (/ (- 1.0 k) 2.0))
43.0ms	(/ 1.0 (sqrt k))
70.0ms	(* (* 2.0 PI) (sqrt n))
51.0ms	(* (* (* 2.0 PI) (sqrt n)) (sqrt n))

simplify81.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	755	1027
1	3088	876
2	5001	848

prune320.0ms

Filtered

142 candidates to 92 candidates (64.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	142	0	142
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	142	9	151

Merged error: 0.0b

Counts

151 → 9

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 2.0 PI) n)
0.3b	(/ 1.0 (sqrt k))
0.4b	(pow (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (/ (- (sqrt 1.0) (sqrt k)) 2.0))
0.4b	(pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

67×	`add-sqr-sqrt` `*-un-lft-identity`
60×	`times-frac`
50×	`pow-unpow`
43×	`add-cube-cbrt`
36×	`sqrt-prod`
24×	`add-exp-log`
15×	`pow1`
12×	`difference-of-squares`
11×	`pow-exp` `add-cbrt-cube`
9×	`prod-exp`
7×	`unpow-prod-down`
6×	`pow-prod-down` `associate-/r*` `distribute-lft-out` `distribute-lft-out--`
4×	`expm1-log1p-u` `pow-pow` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `associate-r` `cbrt-unprod` `div-inv` `associate-/l*` `sqr-pow`
1×	`cbrt-undiv` `frac-2neg` `div-sub` `div-exp` `associate-l` `clear-num` `*-commutative` `pow-sub`

Counts

4 → 152

Calls

4 calls:

5.0ms	(* (* 2.0 PI) n)
4.0ms	(/ 1.0 (sqrt k))
14.0ms	(pow (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (/ (- (sqrt 1.0) (sqrt k)) 2.0))
11.0ms	(pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1))

series1.2s

Counts

4 → 12

Calls

4 calls:

31.0ms	(* (* 2.0 PI) n)
43.0ms	(/ 1.0 (sqrt k))
819.0ms	(pow (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (/ (- (sqrt 1.0) (sqrt k)) 2.0))
286.0ms	(pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1))

simplify70.0ms

Algorithm

egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 1 (36.0ms)

Iter	Nodes	Cost
0	1933	3806
1	5001	3737

prune521.0ms

Filtered

164 candidates to 105 candidates (64.0%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	163	1	164
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	163	10	173

Merged error: 0b

Counts

173 → 10

regimes126.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	12
1	19	12

end0.0ms

sample5.4s

Algorithm

intervals

Results

2.2s	27276×	body	80	nan
905.0ms	10567×	body	80	valid
611.0ms	1012×	body	1280	nan
377.0ms	856×	body	640	nan
343.0ms	2456×	body	80	overflowed
132.0ms	439×	body	320	nan
37.0ms	209×	body	160	nan